Send a test message (SMS) to a specified mobile number whenever a new email arrives. I'm not bothered if the SMS doesn't contain any part of the email, would just like a notification that an email has arrived so the laptop can be booted to check.

This is for my parents who have a very low-traffic account, usually go days without even looking at their laptop and don't have a smartphone, tablet or any other instant-on device (so checking is a bit of a chore).